This paper presents a model-based method for the system identification of a rectangular enclosure with an unknown number of air leakages subjected to uniform external noise, according to the probabilistic approach. The method aims to identify the number and corresponding locations and sizes of air leakages utilizing a set of measured, interior, sound pressure data in the frequency domain. System identification of an enclosure with an unknown number of air leakages is not trivial. Different classes of acoustic models are required to simulate an enclosure with different numbers of leakages. By following the traditional system of identification techniques, the “optimal” class of models is selected by minimizing the discrepancy between the measured and modeled interior sound pressure. By doing this, the most complicated model class (that is, the one with the highest number of uncertain parameters) will always be selected. Therefore, the traditional system identification techniques found in the literature to date cannot be employed to solve this problem. Our proposed system identification methodology relies on the Bayesian information criterion (BIC) to identify accurately the number of leakages in an enclosure. Unlike all deterministic system identification approaches, the proposed methodology aims to calculate the posterior (updated) probability density function (PDF) of leakage locations and sizes. Therefore, the uncertainties introduced by measurement noise and modeling error can be explicitly addressed. The coefficient of variable (COV) of uncertain parameters, which can be easily calculated from the PDF, provides valuable information about the reliability of the identification results.